"mówić" - the simple verb for "to talk", rather one-side (Mówię do ciebie = I am talking to you). Sometimes "to say" and "to tell" are also correct translations depending on the context.
"rozmawiać" is a basic verb for "to talk with someone", "to converse".
"porozmawiać" is like a perfective variant of "rozmawiać", so more like "to have a conversation". "Muszę z nią porozmawiać" = I need to talk with/to her = I need to have a conversation with her.
You made a typo and wrote "rozmówić", but "rozmówić się" is actually also correct, it's just not a common verb and we don't teach it. It's something in the direction of "to discuss some matter with someone".
The tie bar above /tʂ/ is a very important element here. You shouldn't think of it as two separate sounds, but as only one.
To a native speaker this makes quite a big difference.
While I agree that the cz in this sentence could have been pronounced more clearly, it still sounds acceptable to me.
I'm not that much used to listening to Polish yet. The Duolingo audios are still my main source, and usually they pronounce it much more clearly. However, I'm aware of the difference between the sounds in 'czy' and 'trzy' . But still listening to Polish speakers in real life and trying to understand at least a little bit of it often makes me go crazy ;-D